Quantum Mechanics meet Special Relativity

First there’s quantum mechanics, the theory of the very small where determinism in the classical sense breaks down; to get anywhere with an experiment you have to predict in terms of probabilities. Probabilities of specific observations must always be between 0 and 1 and the overall probability of observing something must be 1. Then there’s special relativity in which Galilean relativity breaks down as the speed of light turns out to be the same in all reference frames, you may know it predicts E2=(mc2)2+(pc)2 (that’s right I’m leaving the momentum in because it’s correct to; FYI wikipedia rest mass is Lorentz invariant and therefore not the same as energy which isn’t, are you suggesting photons, which have no mass, have no energy?!…)

Now, showing wikipedia is unreliable aside, these theories describe different things: quantum mechanics deals with things which are very small but not moving very fast and special relativity deals with things which are not very small but which are moving very fast (near light speed: relativistic). But what happens if you want to measure something very small but also relativistic as you might in a particle collider like the LHC?

Well you clearly have to find some way of combining quantum mechanics and special relativity. In fact you don’t because British physicist Paul Dirac did exactly that in 1928, you just have to be able to understand how to solve this equation:

Unless you’ve studied quantum mechanics and special relativity the symbols in Dirac’s equation won’t mean much. However, mathematically what it does is satisfy the key requirement of combining the two scenarios: all the probabilities of observing a particle in a given state will be between 0 and 1 and the total probability of observing a particle at all will be 1. Critically this is now true no matter how fast the particle is moving!

Dirac’s equation tells you more than that. If you solve it for a particle like an electron you find there are four solutions. From quantum mechanics we expect two types of electron with the distinction being the quantum mechanical property of spin. Spin is related to the angular momentum of a particle and the two distinct spin states of electrons can be observed by passing them through magnetic fields. The other two solutions are a complete surprise, they predict so called ‘negative-energy solutions’ which can be interpreted as a particle with identical mass and spin states as the electron but opposite charge. This particle, the antiparticle electron or positron, was first seen experimentally in 1933.

Antiparticles represent a profound prediction of theoretical physics later being confirmed by experiment. All of the fundamental particles listed in the table in the previous post have corresponding antiparticles. Also, as mentioned last time, a class of subatomic particle known as mesons, are formed from quark-antiquark pairs. In fact all of the particles formed from quarks have antiparticle partners by exchanging quark for antiquark and vice versa. For example the antiproton is formed of two antiup quarks and one antidown quark.

The Dirac equation as discussed above concerns particles which exist for all time somewhere in space; however, in experiments particles come into and decay out of existence in fractions of a second. The description of such processes requires a more general form of relativistic quantum mechanics: quantum field theory.